On the existence of an efficient parallel algorithm for a graph theoretic problem
The problem of computing the relation ⊖ among edges of a graph is an important step in algorithms for several graph theoretic problems such as embedding graphs in Cartesian products, decomposing a graph into a product or deciding whether a graph is a binary Hamming graph. By an efficient parallel algorithm we mean one that takes polylogarithmic time using a polynomial number of processors. In this paper we show that there are efficient parallel algorithms for computing the relation ⊖, for computing the equivalence classes of its transitive closure \(\hat \Theta \) and for deciding whether a graph is a binary Hamming graph.
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- A.V.Aho, J.E.Hopcroft, J.D.Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass. 1974Google Scholar
- F.Aurenhammer, J.Hagauer: Computing Equivalence Classes among the Edges of a Graph with Applications, (to appear in Discrete Mathematics)Google Scholar
- F. Aurenhammer, J.Hagauer: Recognizing Binary Hamming Graphs in O(¦V∥E¦) time, (to appear in Discrete Mathematics)Google Scholar
- A.Gibbons, W.Rytter: Efficient Parallel Algorithms, Cambridge University Press 1988Google Scholar
- W.Imrich: Embedding Graphs into Cartesian Products, Graph Theory and Applications: East and West, Annals of the New York Academy of Sciences, vol. 576, (1989) 266–274Google Scholar
- R.E.Tarjan: Data Structures and Network Algorithms, CMBS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia 1983Google Scholar
- P.M.Winkler: Factoring a graph in polynomial time, European Journal of Combinatorics 8 (1987) 209–212Google Scholar
- P.M.Winkler: Isometric Embeddings in Products of Complete Graphs, Discrete Applied Mathematics 7 (1984) 221–225Google Scholar
- J.Žerovnik: A Simple Algorithm for Factoring a Cartesian-Product Graph, Arbeitsberict 5/1991, Institut für Mathematik und Angewandte Geometrie, Montauniversität LeobenGoogle Scholar